for all \(t\ge 0\) . To justify the martingale property of \(\overline{Z}_t^N(Y)\overline{Z}_t^{-1}(Y)\)  one can use, for example, an argument based on Corollary 5.14 in [1]}.
As a result of the above calculations we can deduce that \(\overline{Z}_t^N(Y)\)  is in some sense well-defined, but a biased estimator of the normalization constant. Therefore,
we will focus on the logarithm of the normalization constant, as it is this latter quantity that is used in practical algorithms. We begin by investigating the conditional bias.
